Hilbert modular form data - 2.2.321.1-3.1-m

Formats: - HTML - YAML - JSON - 2024-05-05T21:46:33.070077

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 2, 'dimension': 8, 'disc': 321, 'field_bad_primes': [3, 107], 'field_label': '2.2.321.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.321.1-3.1-m', 'label_nsuffix': 12, 'label_suffix': 'm', 'level_bad_primes': [3], 'level_ideal': '[3, 3, -2*w + 19]', 'level_label': '3.1', 'level_norm': 3, 'parallel_weight': 2, 'short_label': '3.1-m', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -2*w + 19]', -1]], 'hecke_eigenvalues': ['e', '-e^7 - 5*e^5 - 24*e^3 - 5*e', 1, '-19/24*e^7 - 4*e^5 - 19*e^3 - 95/24*e', '1/24*e^7 - 91/24*e', '23/24*e^6 + 5*e^4 + 23*e^2 + 115/24', '25/24*e^6 + 5*e^4 + 23*e^2 + 5/24', '-3/8*e^7 - 2*e^5 - 9*e^3 - 15/8*e', '1/8*e^7 - 107/8*e', '-25/24*e^6 - 5*e^4 - 25*e^2 - 5/24', '25/24*e^6 + 5*e^4 + 25*e^2 + 125/24', '35/24*e^6 + 7*e^4 + 33*e^2 + 7/24', '13/24*e^6 + 3*e^4 + 13*e^2 + 65/24', -12, '-15/4*e^7 - 18*e^5 - 86*e^3 - 3/4*e', '5/4*e^7 + 6*e^5 + 28*e^3 + 1/4*e', '-43/24*e^6 - 9*e^4 - 43*e^2 - 215/24', '-5/24*e^6 - e^4 - 3*e^2 - 1/24', '59/24*e^7 + 12*e^5 + 59*e^3 + 295/24*e', '7/24*e^7 - 829/24*e', '1/6*e^6 - 31/6', '-1/6*e^6 + 79/6', '15/2*e^7 + 36*e^5 + 174*e^3 + 3/2*e', '-5/24*e^7 + 743/24*e', '-193/24*e^7 - 40*e^5 - 193*e^3 - 965/24*e', 14, '161/24*e^7 + 34*e^5 + 161*e^3 + 805/24*e', '-11/24*e^7 + 1049/24*e', '-55/24*e^6 - 11*e^4 - 51*e^2 - 11/24', '-41/24*e^6 - 9*e^4 - 41*e^2 - 205/24', '-1/6*e^6 + 67/6', '1/6*e^6 - 43/6', '-13/24*e^7 + 1327/24*e', '103/24*e^7 + 22*e^5 + 103*e^3 + 515/24*e', '-1/24*e^7 + 235/24*e', '-125/24*e^7 - 26*e^5 - 125*e^3 - 625/24*e', '-29/24*e^7 - 6*e^5 - 29*e^3 - 145/24*e', '-1/24*e^7 + 139/24*e', '1/8*e^7 - 203/8*e', '93/8*e^7 + 58*e^5 + 279*e^3 + 465/8*e', '1/4*e^6 - 99/4', '-1/4*e^6 + 11/4', '15/8*e^6 + 9*e^4 + 45*e^2 + 3/8', '-15/8*e^6 - 9*e^4 - 45*e^2 - 75/8', '77/24*e^6 + 15*e^4 + 77*e^2 + 385/24', '-125/24*e^6 - 25*e^4 - 123*e^2 - 25/24', '-55/24*e^6 - 11*e^4 - 57*e^2 - 11/24', '103/24*e^6 + 21*e^4 + 103*e^2 + 515/24', '-5/3*e^7 - 8*e^5 - 40*e^3 - 1/3*e', '-25/3*e^7 - 40*e^5 - 192*e^3 - 5/3*e', '65/24*e^7 + 14*e^5 + 65*e^3 + 325/24*e', '-11/24*e^7 + 1145/24*e', '85/24*e^6 + 17*e^4 + 75*e^2 + 17/24', '155/24*e^6 + 33*e^4 + 155*e^2 + 775/24', '20/3*e^7 + 32*e^5 + 152*e^3 + 4/3*e', '-20/3*e^7 - 32*e^5 - 152*e^3 - 4/3*e', '119/24*e^6 + 25*e^4 + 119*e^2 + 595/24', '25/24*e^6 + 5*e^4 + 19*e^2 + 5/24', '-181/24*e^7 - 38*e^5 - 181*e^3 - 905/24*e', '7/24*e^7 - 589/24*e', '133/24*e^6 + 27*e^4 + 133*e^2 + 665/24', '-85/24*e^6 - 17*e^4 - 87*e^2 - 17/24', '25/6*e^7 + 20*e^5 + 96*e^3 + 5/6*e', '5/6*e^7 + 4*e^5 + 20*e^3 + 1/6*e', '-119/24*e^6 - 25*e^4 - 119*e^2 - 595/24', '-25/24*e^6 - 5*e^4 - 19*e^2 - 5/24', '59/24*e^6 + 13*e^4 + 59*e^2 + 295/24', '85/24*e^6 + 17*e^4 + 79*e^2 + 17/24', '-67/8*e^7 - 42*e^5 - 201*e^3 - 335/8*e', '1/8*e^7 - 43/8*e', '65/12*e^7 + 26*e^5 + 122*e^3 + 13/12*e', '-155/12*e^7 - 62*e^5 - 296*e^3 - 31/12*e', '47/24*e^7 + 10*e^5 + 47*e^3 + 235/24*e', '-5/24*e^7 + 503/24*e', '-15/8*e^6 - 9*e^4 - 47*e^2 - 3/8', '31/8*e^6 + 19*e^4 + 93*e^2 + 155/8', '-10*e^7 - 48*e^5 - 232*e^3 - 2*e', '-10*e^7 - 48*e^5 - 232*e^3 - 2*e', '-1/12*e^6 - 173/12', '1/12*e^6 - 283/12', '-5/12*e^7 - 2*e^5 - 8*e^3 - 1/12*e', '95/12*e^7 + 38*e^5 + 182*e^3 + 19/12*e', '-1/24*e^7 - 53/24*e', '163/24*e^7 + 34*e^5 + 163*e^3 + 815/24*e', '45/8*e^6 + 27*e^4 + 135*e^2 + 9/8', '-45/8*e^6 - 27*e^4 - 135*e^2 - 225/8', '1/2*e^6 - 43/2', '-1/2*e^6 + 67/2', '15*e^7 + 72*e^5 + 342*e^3 + 3*e', '-15*e^7 - 72*e^5 - 342*e^3 - 3*e', '5/8*e^7 - 439/8*e', '-111/8*e^7 - 70*e^5 - 333*e^3 - 555/8*e', '-31/24*e^6 - 5*e^4 - 31*e^2 - 155/24', '175/24*e^6 + 35*e^4 + 169*e^2 + 35/24', '1/12*e^6 + 101/12', '-1/12*e^6 + 211/12', '17/24*e^7 + 4*e^5 + 17*e^3 + 85/24*e', '-11/24*e^7 + 1193/24*e', '13/24*e^7 - 1471/24*e', '41/24*e^7 + 8*e^5 + 41*e^3 + 205/24*e', '1/8*e^7 - 91/8*e', '-19/8*e^7 - 12*e^5 - 57*e^3 - 95/8*e', -10, '-67/24*e^6 - 15*e^4 - 67*e^2 - 335/24', '-125/24*e^6 - 25*e^4 - 117*e^2 - 25/24', '-155/24*e^7 - 32*e^5 - 155*e^3 - 775/24*e', '-7/24*e^7 + 925/24*e', '-211/24*e^7 - 44*e^5 - 211*e^3 - 1055/24*e', '1/24*e^7 + 101/24*e', '-55/8*e^6 - 33*e^4 - 159*e^2 - 11/8', '7/8*e^6 + 3*e^4 + 21*e^2 + 35/8', '-35/8*e^6 - 21*e^4 - 101*e^2 - 7/8', '3/8*e^6 + e^4 + 9*e^2 + 15/8', '145/8*e^7 + 90*e^5 + 435*e^3 + 725/8*e', '5/8*e^7 - 695/8*e', '-19/24*e^7 + 2305/24*e', '-215/24*e^7 - 44*e^5 - 215*e^3 - 1075/24*e', '67/8*e^7 + 42*e^5 + 201*e^3 + 335/8*e', '-1/8*e^7 + 43/8*e', '-215/24*e^6 - 43*e^4 - 207*e^2 - 43/24', '23/24*e^6 + 3*e^4 + 23*e^2 + 115/24', '-20/3*e^7 - 32*e^5 - 150*e^3 - 4/3*e', '50/3*e^7 + 80*e^5 + 382*e^3 + 10/3*e', '55/6*e^7 + 44*e^5 + 210*e^3 + 11/6*e', '-25/6*e^7 - 20*e^5 - 94*e^3 - 5/6*e', '-1/2*e^6 + 27/2', '1/2*e^6 - 83/2', '175/24*e^6 + 35*e^4 + 165*e^2 + 35/24', '65/24*e^6 + 15*e^4 + 65*e^2 + 325/24', '-109/24*e^7 - 22*e^5 - 109*e^3 - 545/24*e', '-17/24*e^7 + 1979/24*e', '1/8*e^7 - 59/8*e', '-51/8*e^7 - 32*e^5 - 153*e^3 - 255/8*e', '121/24*e^6 + 25*e^4 + 121*e^2 + 605/24', '-25/24*e^6 - 5*e^4 - 29*e^2 - 5/24', '10*e^7 + 48*e^5 + 230*e^3 + 2*e', '2*e^3', '481/24*e^7 + 100*e^5 + 481*e^3 + 2405/24*e', '5/24*e^7 - 1031/24*e', -16, -16, '-1/24*e^7 - 197/24*e', '307/24*e^7 + 64*e^5 + 307*e^3 + 1535/24*e', '59/24*e^7 + 12*e^5 + 59*e^3 + 295/24*e', '7/24*e^7 - 829/24*e', -22, '-35/8*e^6 - 21*e^4 - 105*e^2 - 7/8', '35/8*e^6 + 21*e^4 + 105*e^2 + 175/8', '1/8*e^7 + 3*e^3 + 5/8*e', '5/8*e^7 - 551/8*e', '265/24*e^6 + 53*e^4 + 253*e^2 + 53/24', '23/24*e^6 + 7*e^4 + 23*e^2 + 115/24', '5/8*e^7 - 375/8*e', '-175/8*e^7 - 110*e^5 - 525*e^3 - 875/8*e', '10/3*e^7 + 16*e^5 + 82*e^3 + 2/3*e', '80/3*e^7 + 128*e^5 + 614*e^3 + 16/3*e', '-5/24*e^7 + 887/24*e', '-337/24*e^7 - 70*e^5 - 337*e^3 - 1685/24*e', '-25/8*e^6 - 15*e^4 - 61*e^2 - 5/8', '-87/8*e^6 - 55*e^4 - 261*e^2 - 435/8', '-20/3*e^7 - 32*e^5 - 154*e^3 - 4/3*e', '-10/3*e^7 - 16*e^5 - 78*e^3 - 2/3*e', '125/12*e^7 + 50*e^5 + 240*e^3 + 25/12*e', '25/12*e^7 + 10*e^5 + 50*e^3 + 5/12*e', 14, '85/24*e^6 + 17*e^4 + 87*e^2 + 17/24', '-133/24*e^6 - 27*e^4 - 133*e^2 - 665/24', '-5/8*e^7 + 551/8*e', '-1/8*e^7 - 3*e^3 - 5/8*e', '107/24*e^7 + 22*e^5 + 107*e^3 + 535/24*e', '7/24*e^7 - 877/24*e', '103/24*e^6 + 21*e^4 + 103*e^2 + 515/24', '-55/24*e^6 - 11*e^4 - 57*e^2 - 11/24'], 'hecke_polynomial': 'x^8 + 5*x^6 + 24*x^4 + 5*x^2 + 1', 'label': '2.2.321.1-3.1-m'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 2, 'discriminant': 321, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[2, 2, w + 1]', '[3, 3, -2*w + 19]', '[4, 2, 2]', '[4, 4, w]', '[4, 4, w + 3]', '[5, 5, w]', '[5, 5, w + 4]', '[6, 6, w + 1]', '[6, 6, w + 4]', '[8, 4, 2*w]', '[8, 4, 2*w + 2]', '[8, 8, -w - 8]', '[8, 8, -w + 9]', '[9, 3, 3]', '[10, 10, -w + 10]', '[10, 10, w + 4]', '[10, 10, w + 5]', '[10, 10, w + 9]', '[12, 6, -4*w + 38]', '[12, 12, w + 4]', '[12, 12, w + 7]', '[13, 13, w + 1]', '[13, 13, w + 11]', '[15, 15, w + 4]', '[15, 15, w + 10]', '[16, 4, 4]', '[16, 8, 2*w]', '[16, 8, 2*w + 6]', '[16, 16, w]', '[16, 16, w + 15]', '[17, 17, w + 3]', '[17, 17, w + 13]', '[18, 6, 3*w]', '[18, 6, 3*w + 3]', '[19, 19, w + 6]', '[19, 19, w + 12]', '[20, 10, 2*w]', '[20, 10, 2*w + 8]', '[20, 20, w]', '[20, 20, -3*w + 28]', '[20, 20, -3*w - 25]', '[20, 20, w + 19]', '[24, 12, 2*w + 2]', '[24, 12, 2*w + 8]', '[24, 24, -w - 7]', '[24, 24, -w + 8]', '[25, 5, 5]', '[25, 25, w + 5]', '[25, 25, w + 19]', '[26, 26, 5*w - 47]', '[26, 26, w + 11]', '[26, 26, w + 14]', '[26, 26, 5*w + 42]', '[27, 9, -6*w + 57]', '[30, 30, w + 4]', '[30, 30, w + 10]', '[30, 30, -w + 11]', '[30, 30, w + 25]', '[32, 8, 4*w]', '[32, 8, 4*w + 4]', '[32, 16, -2*w - 16]', '[32, 16, -2*w + 18]', '[32, 32, w + 15]', '[32, 32, w + 16]', '[34, 34, w + 3]', '[34, 34, 3*w - 29]', '[34, 34, -3*w - 26]', '[34, 34, w + 30]', '[36, 6, 6]', '[36, 12, 3*w]', '[36, 12, 3*w + 9]', '[37, 37, w + 2]', '[37, 37, w + 34]', '[38, 38, -w - 6]', '[38, 38, w + 12]', '[38, 38, w + 25]', '[38, 38, w - 7]', '[39, 39, w + 1]', '[39, 39, w + 37]', '[40, 20, -2*w + 20]', '[40, 20, 2*w + 8]', '[40, 20, 2*w + 10]', '[40, 20, 2*w + 18]', '[40, 40, w]', '[40, 40, w + 15]', '[40, 40, w + 24]', '[40, 40, w + 39]', '[45, 15, 3*w]', '[45, 15, 3*w + 12]', '[48, 12, -8*w + 76]', '[48, 24, 2*w + 8]', '[48, 24, 2*w + 14]', '[48, 48, w + 16]', '[48, 48, w + 31]', '[49, 7, -7]', '[50, 10, 5*w]', '[50, 10, 5*w + 5]', '[50, 50, -w - 5]', '[50, 50, w + 19]', '[50, 50, w + 30]', '[50, 50, -w + 6]', '[51, 51, w + 13]', '[51, 51, w + 37]', '[52, 26, 2*w + 2]', '[52, 26, 2*w + 22]', '[52, 52, -w - 11]', '[52, 52, w + 24]', '[52, 52, w + 27]', '[52, 52, w - 12]', '[54, 18, 3*w + 3]', '[54, 18, 3*w + 12]', '[57, 57, w + 25]', '[57, 57, w + 31]', '[59, 59, -4*w - 33]', '[59, 59, 4*w - 37]', '[60, 30, 2*w + 8]', '[60, 30, 2*w + 20]', '[60, 60, -w - 4]', '[60, 60, w + 19]', '[60, 60, w + 40]', '[60, 60, -w + 5]', '[61, 61, w + 28]', '[61, 61, w + 32]', '[64, 8, 8]', '[64, 16, 4*w]', '[64, 16, 4*w + 12]', '[64, 32, 2*w]', '[64, 32, 2*w + 30]', '[64, 64, -5*w + 48]', '[64, 64, 5*w + 43]', '[65, 65, w + 14]', '[65, 65, 2*w - 17]', '[65, 65, 2*w + 15]', '[65, 65, w + 50]', '[68, 34, 2*w + 6]', '[68, 34, 2*w + 26]', '[68, 68, w + 3]', '[68, 68, w + 20]', '[68, 68, w + 47]', '[68, 68, w - 4]', '[71, 71, w + 22]', '[71, 71, w + 48]', '[72, 12, 6*w]', '[72, 12, 6*w + 6]', '[72, 24, -3*w - 24]', '[72, 24, -3*w + 27]', '[74, 74, -w - 2]', '[74, 74, w + 34]', '[74, 74, w + 39]', '[74, 74, w - 3]', '[75, 15, -10*w + 95]', '[75, 75, w + 19]', '[75, 75, w + 55]', '[76, 38, 2*w + 12]', '[76, 38, 2*w + 24]', '[76, 76, -w - 12]', '[76, 76, w + 31]', '[76, 76, w + 44]', '[76, 76, -w + 13]', '[78, 78, w + 1]', '[78, 78, w + 37]', '[78, 78, w + 40]', '[78, 78, w - 2]', '[79, 79, 2*w - 21]', '[79, 79, 2*w + 19]', '[80, 20, 4*w]', '[80, 20, 4*w + 16]', '[80, 40, 2*w]', '[80, 40, -6*w + 56]', '[80, 40, -6*w - 50]', '[80, 40, 2*w + 38]', '[80, 80, -w]', '[80, 80, w + 15]', '[80, 80, w + 64]', '[80, 80, -w + 1]', '[81, 9, 9]', '[85, 85, w + 20]', '[85, 85, -4*w - 35]', '[85, 85, 4*w - 39]', '[85, 85, w + 64]', '[90, 30, -3*w + 30]', '[90, 30, 3*w + 12]', '[90, 30, 3*w + 15]', '[90, 30, 3*w + 27]', '[95, 95, w + 25]', '[95, 95, -8*w - 67]', '[95, 95, 8*w - 75]', '[95, 95, w + 69]', '[96, 24, 4*w + 4]', '[96, 24, 4*w + 16]', '[96, 48, -2*w - 14]', '[96, 48, -2*w + 16]', '[96, 96, w + 16]', '[96, 96, w + 79]', '[98, 14, 7*w]', '[98, 14, 7*w + 7]', '[100, 10, 10]', '[100, 20, 5*w]', '[100, 20, 5*w + 15]', '[100, 50, 2*w + 10]', '[100, 50, 2*w + 38]', '[100, 100, -7*w + 67]', '[100, 100, w + 44]', '[100, 100, w + 55]', '[100, 100, 7*w + 60]', '[102, 102, -w - 13]', '[102, 102, w + 37]', '[102, 102, w + 64]', '[102, 102, w - 14]', '[104, 52, 10*w - 94]', '[104, 52, 2*w + 22]', '[104, 52, 2*w + 28]', '[104, 52, 10*w + 84]', '[104, 104, w + 24]', '[104, 104, w + 40]', '[104, 104, w + 63]', '[104, 104, w + 79]', '[107, 107, 12*w - 113]', '[108, 18, -12*w + 114]', '[108, 36, 3*w + 12]', '[108, 36, 3*w + 21]', '[111, 111, w + 34]', '[111, 111, w + 76]', '[113, 113, w + 17]', '[113, 113, w + 95]', '[114, 114, w + 25]', '[114, 114, 31*w - 293]', '[114, 114, -5*w + 46]', '[114, 114, w + 88]', '[117, 39, 3*w + 3]', '[117, 39, 3*w + 33]', '[118, 118, w + 23]', '[118, 118, w + 35]', '[118, 118, w + 82]', '[118, 118, w + 94]', '[120, 60, 2*w + 8]', '[120, 60, 2*w + 20]', '[120, 60, -2*w + 22]', '[120, 60, 2*w + 50]', '[120, 120, w + 40]', '[120, 120, w + 55]', '[120, 120, w + 64]', '[120, 120, w + 79]', '[121, 11, -11]', '[122, 122, w + 28]', '[122, 122, -3*w + 26]', '[122, 122, 3*w + 23]', '[122, 122, w + 93]', '[125, 25, 5*w]', '[125, 25, 5*w + 20]', '[125, 125, -2*w + 15]', '[125, 125, -2*w - 13]', '[128, 16, 8*w]', '[128, 16, 8*w + 8]', '[128, 32, -4*w - 32]', '[128, 32, -4*w + 36]', '[128, 64, 2*w + 30]', '[128, 64, 2*w + 32]', '[128, 128, w + 47]', '[128, 128, w + 80]', '[130, 130, -w - 14]', '[130, 130, w + 24]', '[130, 130, w + 40]', '[130, 130, w + 50]', '[130, 130, w + 79]', '[130, 130, w + 89]', '[130, 130, w + 105]', '[130, 130, w - 15]', '[131, 131, w + 18]', '[131, 131, w + 112]', '[135, 45, 3*w + 12]', '[135, 45, 3*w + 30]', '[136, 68, 2*w + 6]', '[136, 68, 6*w - 58]', '[136, 68, -6*w - 52]', '[136, 68, 2*w + 60]', '[136, 136, w + 47]', '[136, 136, w + 64]', '[136, 136, w + 71]', '[136, 136, w + 88]', '[142, 142, 9*w - 86]', '[142, 142, w + 48]', '[142, 142, w + 93]', '[142, 142, -9*w - 77]', '[144, 12, 12]', '[144, 24, 6*w]', '[144, 24, 6*w + 18]', '[144, 48, 3*w]', '[144, 48, 3*w + 45]', '[147, 21, 14*w - 133]', '[148, 74, 2*w + 4]', '[148, 74, 2*w + 68]', '[148, 148, -3*w + 31]', '[148, 148, w + 71]', '[148, 148, w + 76]', '[148, 148, -3*w - 28]', '[150, 30, 5*w + 5]', '[150, 30, 5*w + 20]', '[150, 150, w + 19]', '[150, 150, -7*w + 65]', '[150, 150, -7*w - 58]', '[150, 150, w + 130]', '[151, 151, w + 43]', '[151, 151, w + 107]', '[152, 76, -2*w - 12]', '[152, 76, 2*w + 24]', '[152, 76, 2*w + 50]', '[152, 76, 2*w - 14]', '[152, 152, w + 31]', '[152, 152, w + 63]', '[152, 152, w + 88]', '[152, 152, w + 120]', '[153, 51, 3*w + 9]', '[153, 51, 3*w + 39]', '[156, 78, 2*w + 2]', '[156, 78, 2*w + 74]', '[156, 156, -5*w - 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158]', '[1888, 944, 2*w - 48]', '[1888, 1888, w + 271]', '[1888, 1888, w + 495]', '[1888, 1888, w + 1392]', '[1888, 1888, w + 1616]', '[1889, 1889, w + 732]', '[1889, 1889, w + 1156]', '[1894, 1894, w + 87]', '[1894, 1894, w + 859]', '[1894, 1894, w + 1034]', '[1894, 1894, w + 1806]', '[1896, 948, 2*w + 98]', '[1896, 948, 2*w + 374]', '[1896, 948, 2*w + 572]', '[1896, 948, 2*w + 848]', '[1896, 1896, 35*w - 328]', '[1896, 1896, -5*w - 8]', '[1896, 1896, 5*w - 13]', '[1896, 1896, -35*w - 293]', '[1900, 190, 10*w + 60]', '[1900, 190, 10*w + 120]', '[1900, 380, -5*w - 60]', '[1900, 380, 5*w + 155]', '[1900, 380, 5*w + 220]', '[1900, 380, -5*w + 65]', '[1900, 950, 2*w + 88]', '[1900, 950, 12*w - 122]', '[1900, 950, 12*w + 110]', '[1900, 950, 2*w + 860]', '[1900, 1900, w + 44]', '[1900, 1900, w + 519]', '[1900, 1900, w + 544]', '[1900, 1900, w + 880]', '[1900, 1900, w + 1019]', '[1900, 1900, w + 1355]', '[1900, 1900, w + 1380]', '[1900, 1900, w - 45]', '[1901, 1901, w + 222]', '[1901, 1901, w + 1678]', '[1902, 1902, w + 157]', '[1902, 1902, w + 793]', '[1902, 1902, w + 1108]', '[1902, 1902, w + 1744]', '[1906, 1906, w + 151]', '[1906, 1906, w + 801]', '[1906, 1906, w + 1104]', '[1906, 1906, w + 1754]', '[1907, 1907, -28*w + 261]', '[1907, 1907, 92*w - 869]', '[1910, 1910, w + 169]', '[1910, 1910, w + 360]', '[1910, 1910, 19*w - 174]', '[1910, 1910, w + 785]', '[1910, 1910, w + 1124]', '[1910, 1910, 19*w + 155]', '[1910, 1910, w + 1549]', '[1910, 1910, w + 1740]', '[1911, 273, 7*w + 7]', '[1911, 273, 7*w + 259]', '[1913, 1913, w + 62]', '[1913, 1913, w + 1850]', '[1916, 958, 2*w + 386]', '[1916, 958, 2*w + 570]', '[1916, 1916, w + 672]', '[1916, 1916, 5*w - 12]', '[1916, 1916, -5*w - 7]', '[1916, 1916, w + 1243]', '[1917, 639, 3*w + 66]', '[1917, 639, 3*w + 570]', '[1920, 240, 8*w + 32]', '[1920, 240, 8*w + 80]', '[1920, 240, -8*w + 88]', '[1920, 240, 8*w + 200]', '[1920, 480, 4*w + 160]', '[1920, 480, 4*w + 220]', '[1920, 480, 4*w + 256]', '[1920, 480, 4*w + 316]', '[1920, 960, 2*w + 158]', '[1920, 960, -26*w + 250]', '[1920, 960, 26*w + 224]', '[1920, 960, 2*w + 800]', '[1920, 1920, w + 175]', '[1920, 1920, 7*w + 73]', '[1920, 1920, -7*w + 80]', '[1920, 1920, w + 1744]', '[1921, 1921, w + 547]', '[1921, 1921, 40*w + 341]', '[1921, 1921, -40*w + 381]', '[1921, 1921, w + 1373]', '[1922, 62, 31*w]', '[1922, 62, 31*w + 31]', '[1923, 1923, w + 784]', '[1923, 1923, w + 1138]', '[1924, 962, 2*w + 152]', '[1924, 962, 32*w + 274]', '[1924, 962, 32*w - 306]', '[1924, 962, 2*w + 808]', '[1924, 1924, -57*w - 484]', '[1924, 1924, w + 219]', '[1924, 1924, w + 404]', '[1924, 1924, w + 700]', '[1924, 1924, w + 1223]', '[1924, 1924, w + 1519]', '[1924, 1924, w + 1704]', '[1924, 1924, -57*w + 541]', '[1926, 642, 3*w + 159]', '[1926, 642, 3*w + 480]', '[1928, 964, 2*w + 170]', '[1928, 964, 6*w - 34]', '[1928, 964, -6*w - 28]', '[1928, 964, 2*w + 792]', '[1928, 1928, w + 567]', '[1928, 1928, w + 808]', '[1928, 1928, w + 1119]', '[1928, 1928, w + 1360]', '[1929, 1929, w + 694]', '[1929, 1929, w + 1234]', '[1930, 1930, w + 274]', '[1930, 1930, w + 304]', '[1930, 1930, -3*w - 50]', '[1930, 1930, -17*w - 150]', '[1930, 1930, 17*w - 167]', '[1930, 1930, 3*w - 53]', '[1930, 1930, w + 1625]', '[1930, 1930, w + 1655]', '[1931, 1931, w + 340]', '[1931, 1931, w + 1590]', '[1934, 1934, -5*w - 6]', '[1934, 1934, w + 578]', '[1934, 1934, w + 1355]', '[1934, 1934, 5*w - 11]', '[1936, 44, 44]', '[1936, 88, 22*w]', '[1936, 88, 22*w + 66]', '[1936, 176, 11*w]', '[1936, 176, 11*w + 165]', '[1938, 1938, w + 88]', '[1938, 1938, 13*w - 131]', '[1938, 1938, w + 829]', '[1938, 1938, w + 880]', '[1938, 1938, w + 1057]', '[1938, 1938, w + 1108]', '[1938, 1938, 13*w + 118]', '[1938, 1938, w + 1849]', '[1941, 1941, 10*w - 83]', '[1941, 1941, 10*w + 73]', '[1942, 1942, w + 176]', '[1942, 1942, 29*w - 278]', '[1942, 1942, 89*w - 843]', '[1942, 1942, w + 1765]', '[1944, 108, 18*w + 18]', '[1944, 108, 18*w + 72]', '[1944, 216, -9*w - 63]', '[1944, 216, -9*w + 72]', '[1945, 1945, w + 445]', '[1945, 1945, w + 834]', '[1945, 1945, w + 1110]', '[1945, 1945, w + 1499]', '[1950, 390, 5*w + 5]', '[1950, 390, 5*w + 185]', '[1950, 390, 5*w + 200]', '[1950, 390, 5*w - 10]', '[1950, 1950, 37*w + 310]', '[1950, 1950, w + 469]', '[1950, 1950, w + 505]', '[1950, 1950, w + 544]', '[1950, 1950, w + 1405]', '[1950, 1950, w + 1444]', '[1950, 1950, w + 1480]', '[1950, 1950, 37*w - 347]', '[1951, 1951, w + 279]', '[1951, 1951, w + 1671]', '[1952, 488, 4*w + 112]', '[1952, 488, -12*w + 104]', '[1952, 488, 12*w + 92]', '[1952, 488, 4*w + 372]', '[1952, 976, 2*w + 64]', '[1952, 976, 2*w + 430]', '[1952, 976, 2*w + 544]', '[1952, 976, 2*w + 910]', '[1952, 1952, 7*w - 48]', '[1952, 1952, w + 943]', '[1952, 1952, w + 1008]', '[1952, 1952, -7*w - 41]', '[1956, 978, 160*w - 1514]', '[1956, 978, 16*w - 158]', '[1956, 1956, w + 559]', '[1956, 1956, w + 907]', '[1956, 1956, w + 1048]', '[1956, 1956, w + 1396]', '[1960, 140, 14*w - 140]', '[1960, 140, 14*w + 56]', '[1960, 140, 14*w + 70]', '[1960, 140, -14*w - 126]', '[1960, 280, 7*w]', '[1960, 280, 7*w + 105]', '[1960, 280, 7*w + 168]', '[1960, 280, 7*w + 273]', '[1963, 1963, -118*w - 999]', '[1963, 1963, w + 560]', '[1963, 1963, w + 1402]', '[1963, 1963, -118*w + 1117]', '[1964, 982, 2*w + 198]', '[1964, 982, 2*w + 782]', '[1964, 1964, w + 99]', '[1964, 1964, 5*w - 9]', '[1964, 1964, -5*w - 4]', '[1964, 1964, w + 1864]', '[1965, 1965, w + 280]', '[1965, 1965, -4*w - 55]', '[1965, 1965, 4*w - 59]', '[1965, 1965, w + 1684]', '[1966, 1966, -15*w - 134]', '[1966, 1966, w + 842]', '[1966, 1966, w + 1123]', '[1966, 1966, 15*w - 149]', '[1975, 395, 10*w - 105]', '[1975, 395, 10*w + 95]', '[1975, 1975, w + 444]', '[1975, 1975, w + 819]', '[1975, 1975, w + 1155]', '[1975, 1975, w + 1530]', '[1976, 988, 2*w + 100]', '[1976, 988, 18*w + 146]', '[1976, 988, 2*w + 366]', '[1976, 988, 2*w + 392]', '[1976, 988, 2*w + 594]', '[1976, 988, 2*w + 620]', '[1976, 988, -18*w + 164]', '[1976, 988, 2*w + 886]', '[1976, 1976, w + 63]', '[1976, 1976, w + 183]', '[1976, 1976, -25*w + 232]', '[1976, 1976, -5*w - 3]', '[1976, 1976, 5*w - 8]', '[1976, 1976, 25*w + 207]', '[1976, 1976, w + 1792]', '[1976, 1976, w + 1912]', '[1977, 1977, 122*w - 1153]', '[1977, 1977, -22*w + 203]', '[1983, 1983, 2*w - 49]', '[1983, 1983, -2*w - 47]', '[1985, 1985, w + 109]', '[1985, 1985, w + 684]', '[1985, 1985, w + 1300]', '[1985, 1985, w + 1875]', '[1986, 1986, w + 199]', '[1986, 1986, 5*w - 7]', '[1986, 1986, -5*w - 2]', '[1986, 1986, w + 1786]', '[1987, 1987, w + 614]', '[1987, 1987, w + 1372]', '[1989, 663, 3*w + 111]', '[1989, 663, -6*w + 33]', '[1989, 663, -6*w - 27]', '[1989, 663, 3*w + 549]', '[1990, 1990, -w - 45]', '[1990, 1990, w + 244]', '[1990, 1990, w + 750]', '[1990, 1990, w + 949]', '[1990, 1990, w + 1040]', '[1990, 1990, w + 1239]', '[1990, 1990, w + 1745]', '[1990, 1990, w - 46]', '[1994, 1994, -5*w - 1]', '[1994, 1994, w + 597]', '[1994, 1994, w + 1396]', '[1994, 1994, 5*w - 6]', '[1997, 1997, w + 911]', '[1997, 1997, w + 1085]', '[1998, 666, 3*w + 102]', '[1998, 666, -39*w + 366]', '[1998, 666, 69*w - 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989]', '[9985, 9985, w + 8899]', '[9990, 3330, -3*w - 102]', '[9990, 3330, 3*w + 435]', '[9990, 3330, 3*w + 1227]', '[9990, 3330, 3*w + 1560]', '[9990, 3330, 3*w + 1767]', '[9990, 3330, 3*w + 2100]', '[9990, 3330, 3*w + 2892]', '[9990, 3330, -3*w + 105]', '[9993, 9993, -8*w - 119]', '[9993, 9993, 8*w - 127]', '[9996, 714, 14*w + 182]', '[9996, 714, 14*w + 518]', '[9996, 1428, -77*w - 644]', '[9996, 1428, 7*w + 616]', '[9996, 1428, 7*w + 805]', '[9996, 1428, -77*w + 721]', '[10000, 100, 100]', '[10000, 200, 50*w]', '[10000, 200, 50*w + 150]', '[10000, 400, 25*w]', '[10000, 400, 25*w + 375]', '[10000, 500, 20*w + 100]', '[10000, 500, 20*w + 380]', '[10000, 1000, -70*w + 670]', '[10000, 1000, 10*w + 440]', '[10000, 1000, 10*w + 550]', '[10000, 1000, 70*w + 600]', '[10000, 2000, 5*w + 400]', '[10000, 2000, 15*w + 160]', '[10000, 2000, -15*w + 175]', '[10000, 2000, 5*w + 1595]', '[10000, 2500, 4*w + 720]', '[10000, 2500, 4*w + 1776]', '[10000, 5000, 2*w + 360]', '[10000, 5000, -22*w + 232]', '[10000, 5000, 22*w + 210]', '[10000, 5000, 2*w + 4638]', '[10000, 10000, 13*w + 147]', '[10000, 10000, w + 2944]', '[10000, 10000, w + 7055]', '[10000, 10000, -13*w + 160]'], 'label': '2.2.321.1', 'narrow_class_no': 6, 'primes': ['[2, 2, w]', '[2, 2, w + 1]', '[3, 3, -2*w + 19]', '[5, 5, w]', '[5, 5, w + 4]', '[13, 13, w + 1]', '[13, 13, w + 11]', '[17, 17, w + 3]', '[17, 17, w + 13]', '[19, 19, w + 6]', '[19, 19, w + 12]', '[37, 37, w + 2]', '[37, 37, w + 34]', '[49, 7, -7]', '[59, 59, -4*w - 33]', '[59, 59, 4*w - 37]', '[61, 61, w + 28]', '[61, 61, w + 32]', '[71, 71, w + 22]', '[71, 71, w + 48]', '[79, 79, 2*w - 21]', '[79, 79, 2*w + 19]', '[107, 107, 12*w - 113]', '[113, 113, w + 17]', '[113, 113, w + 95]', '[121, 11, -11]', '[131, 131, w + 18]', '[131, 131, w + 112]', '[151, 151, w + 43]', '[151, 151, w + 107]', '[163, 163, 2*w - 23]', '[163, 163, -2*w - 21]', '[167, 167, w + 66]', '[167, 167, w + 100]', '[173, 173, w + 59]', '[173, 173, w + 113]', '[179, 179, w + 60]', '[179, 179, w + 118]', '[191, 191, w + 21]', '[191, 191, w + 169]', '[193, 193, 32*w - 303]', '[193, 193, 8*w - 77]', '[199, 199, w + 45]', '[199, 199, w + 153]', '[223, 223, w + 52]', '[223, 223, w + 170]', '[241, 241, w + 85]', '[241, 241, w + 155]', '[257, 257, 2*w - 9]', '[257, 257, -2*w - 7]', '[269, 269, w + 101]', '[269, 269, w + 167]', '[271, 271, w + 104]', '[271, 271, w + 166]', '[281, 281, -10*w + 93]', '[281, 281, 38*w - 359]', '[283, 283, w + 98]', '[283, 283, w + 184]', '[311, 311, w + 26]', '[311, 311, w + 284]', '[313, 313, w + 36]', '[313, 313, w + 276]', '[317, 317, 2*w - 3]', '[317, 317, -2*w - 1]', '[331, 331, w + 131]', '[331, 331, w + 199]', '[337, 337, w + 127]', '[337, 337, w + 209]', '[347, 347, w + 46]', '[347, 347, w + 300]', '[353, 353, 34*w - 321]', '[353, 353, -14*w + 131]', '[359, 359, w + 156]', '[359, 359, w + 202]', '[373, 373, w + 67]', '[373, 373, w + 305]', '[389, 389, 6*w - 53]', '[389, 389, 6*w + 47]', '[397, 397, 4*w + 39]', '[397, 397, -4*w + 43]', '[401, 401, -18*w + 169]', '[401, 401, 30*w - 283]', '[419, 419, w + 126]', '[419, 419, w + 292]', '[421, 421, w + 65]', '[421, 421, w + 355]', '[439, 439, 10*w - 97]', '[439, 439, -10*w - 87]', '[443, 443, 4*w - 31]', '[443, 443, -4*w - 27]', '[449, 449, w + 182]', '[449, 449, w + 266]', '[457, 457, w + 135]', '[457, 457, w + 321]', '[463, 463, 2*w - 29]', '[463, 463, -2*w - 27]', '[479, 479, w + 193]', '[479, 479, w + 285]', '[491, 491, w + 99]', '[491, 491, w + 391]', '[521, 521, w + 33]', '[521, 521, w + 487]', '[529, 23, -23]', '[547, 547, w + 74]', '[547, 547, w + 472]', '[557, 557, w + 58]', '[557, 557, w + 498]', '[563, 563, w + 253]', '[563, 563, w + 309]', '[571, 571, w + 241]', '[571, 571, w + 329]', '[577, 577, w + 96]', '[577, 577, w + 480]', '[593, 593, w + 248]', '[593, 593, w + 344]', '[617, 617, w + 61]', '[617, 617, w + 555]', '[641, 641, w + 143]', '[641, 641, w + 497]', '[643, 643, w + 51]', '[643, 643, w + 591]', '[647, 647, 8*w - 71]', '[647, 647, 8*w + 63]', '[659, 659, 4*w - 27]', '[659, 659, -4*w - 23]', '[661, 661, 44*w - 417]', '[661, 661, 20*w - 191]', '[691, 691, w + 91]', '[691, 691, w + 599]', '[701, 701, w + 38]', '[701, 701, w + 662]', '[719, 719, w + 303]', '[719, 719, w + 415]', '[727, 727, w + 295]', '[727, 727, w + 431]', '[773, 773, -6*w - 43]', '[773, 773, 6*w - 49]', '[809, 809, w + 220]', '[809, 809, w + 588]', '[811, 811, -10*w - 89]', '[811, 811, 10*w - 99]', '[821, 821, w + 41]', '[821, 821, w + 779]', '[827, 827, w + 177]', '[827, 827, w + 649]', '[841, 29, -29]', '[859, 859, w + 318]', '[859, 859, w + 540]', '[863, 863, w + 42]', '[863, 863, w + 820]', '[883, 883, w + 173]', '[883, 883, w + 709]', '[887, 887, w + 73]', '[887, 887, w + 813]', '[911, 911, 8*w - 69]', '[911, 911, 8*w + 61]', '[929, 929, w + 251]', '[929, 929, w + 677]', '[937, 937, w + 372]', '[937, 937, w + 564]', '[947, 947, 12*w + 97]', '[947, 947, 12*w - 109]', '[953, 953, 6*w - 47]', '[953, 953, -6*w - 41]', '[961, 31, -31]', '[967, 967, w + 388]', '[967, 967, w + 578]', '[971, 971, w + 176]', '[971, 971, w + 794]', '[983, 983, w + 140]', '[983, 983, w + 842]', '[997, 997, w + 399]', '[997, 997, w + 597]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-80, -1, 1], 'conductor': 321, 'degree': 2, 'dirichlet_group': [1, 320], 'disc_abs': 321, 'disc_rad': 321, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [0]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 17.916472867168917, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.321.1', 'local_algs': ['3.2.1.2', '107.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 107], 'rd': 17.9164728672, 'regulator': {'__RealLiteral__': 0, 'data': '6.06377980031', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 24 a + 203 \\)'], 'used_grh': False, 'zk': ['1', 'a']}